I think; therefore I am.
I speak three fluent languages and is learning a fourth, which is kind of unique.

Grammar and its nuance errors are the banes of even prolific writers.

I have made an easy (and a dash of humorous) explanation for your information. If you get confused along the way, there are examples (yay!) to help you understand.

The basic of grammar is to understand the following 3 categories:
-Three kinds of verbs: Action (the most common), Helping (helps other action verbs), and Linking (links subject to their compliments)
-Two kinds of clauses: Independent and Dependent
-Three kinds of sentences: Simple, Complex, Compound

First of all, an independent clause has two major components: subject and verb(predicate). It must have those two, no exceptions. The optional components that it can also have are: direct object(s), subject complement(s), or modifier(s).
example1: Trixie is performing ("Trixie" = subject; "is" = helping verb; "performing" = action verb; no direct object)
example2: Trixie is performing and catching (same as above, except with two action verbs)
example3: Twilight is a friend ("Twilight" = subject; "is" = linking verb; "friend" = subject complement)
example4: Twilight and Dashie are friends and companions (same as above, except with two subjects and two subject complements)
*subject complements are adjectives, nouns, or pronouns that follow a linking verb. If the sub. complement is a pronoun, use the subjective form of the pronoun (he, she, who, etc).

On the other hoof, a dependent clause (sometimes called a subordinate clause) contains one more thing other than subjects and verbs. It has a subordinating conjunction in front that marks it and ties it with an independent clause.
example1: because Trixie catches rotten tomatoes ("because" = sub conjunction; "Trixie" = subject; "catches" = action verb; "tomatoes" = direct object)
example2: if she is a unicorn ("if" = sub conjunction; "she" = subject; "is" = linking verb; "unicorn" = subject complement)

Next, I will explain a sub-category of dependent clauses.
Relative pronouns (that, who, which, where, whom, etc) can be used as subordinating conjunctions; in that case they also play the role of a noun within that clause. This kind of dependent clause is called a relative clause.
example3: where she stood gracefully ("where" is both a subordinating conjunction and the object of the dependent clause)
example4: which was made fastidiously ("which" both the subject of the dependent clause and the subordinating conjunction)
Some subordinating conjunctions are also prepositions too, so don't let that confuse you. Remember, a clause must always have at least one verb!
example5: before the storm started ("before" is a sub conjunction here)
prepositional-phrase: before the storm ("before" is a preposition here)

Now, there are three types of sentences.

- Simple sentences contain a single independent clause. One exception is if it's an imperative statement like "Hand me the apple." where the subject is omitted. An interjection like "Objection!" followed by a punctuation mark are used in writtings, but are not classified as complete sentences.

Simple sentences are not always "short". I can use multiple subjects and verbs and add a whole buncha prepositions in. As long as I never use a subordinating conjunction nor start a new independent clause, it is a simple sentence! It's pretty funny.
ex. "Twilight Sparkle and Rainbow Dash cuddled, nuzzled, and read together after a long, fateful day inside the nostalgic Golden Oak Library next to the warmth of the hearth under the idyllic starlit night."
:)

- Complex sentences contain an independent clause and a dependent clause. They can be in any order, or even imbedded in each other (in some cases of relative clauses).
Before I get to the explanation, consider this analogy:

The independent clause is strong and bold, like Rainbow Dash. The dependent clause is bashful and diffident, like Fluttershy. As a storm is approaching, if Fluttershy is in front, she needs a comma to hold on to give her confidence.

Whenever the dependent clause comes first, you must seperate the clauses with a comma. When the dependent clause is following the independent clause, you don't use comma(s) to seperate the clauses. There is one exception: if the dependent clause is a non-essential relative clause, you need the comma(s) as if you're treating it as a parenthetical element.
What makes a relative clause essential? It all depends on what the relative clause is describing. If it is describing a common/general noun (for example, pony), then the relative clause is essential to defining the noun that it is talking about.
example1: The sonic rainboom was performed by the pony who is adroit. (the relative clause "who is adroit" is essential.)
But if it is describing a proper/specific noun (for example, Rainbow Dash), then the relative clause is non-essential because the name "Rainbow Dash" is already awesome enough to let us know what the relative clause is describing.
example2: The sonic rainboom was performed by Rainbow Dash, who is adroit. (the relative clause "who is adroit" is non-essential.)

That's a lot of information! Luckily, Twilight Sparkle had organized a handy flowchart.

Here are some examples of complex sentences, with the dependent clause underlined:
- dependent clause + comma + independent clause:
Because Fluttershy is hungry, she eats lunch.
- independent clause + dependent clause:
Fluttershy eats lunch if she is hungry.
- relative clause after the independent clause's object:
Rarity abandoned Tom, which is the name of her rock disguised as a diamond..
- relative clause after independent clause's subject:
The clover that Fluttershy brought for Rainbow Dash is surprisingly delicious.
- relative clause before the independent clause:
Where a storm is brewing, Fluttershy looked toward the gulf.

One thing to note, fragments are lonely dependent clause(s) hanging about without any independent clause preceding or following it, a.k.a. incomplete sentences.

- Compound sentences contain two or more independent clauses. Each gap between independent clauses must be linked by a comma plus a coordinating conjunction.
(independent clause + comma + coord conjucton + independent clause)
The seven coordinating conjunctions are "for, and, nor, but, or, yet, so". They can be remembered using the acronym "FANBOYS". When no comma or coordinating conjunction is present, it is a run-on.
CORRECT: Rainbow Dash ate flowers, and she drank cider as well.
run-on1: Rainbow Dash ate flowers she drank cider as well.
run-on2: Rainbow Dash ate flowers, she drank cider as well. (also known as "comma splice", debatable)
run-on3: Rainbow Dash ate flowers and she drank cider as well. (this run-on is often overlooked. if any subject is seen after the coord conjunction, always put a comma before the conjunction. if no subject follows the coord conjunction, no comma needed)
solution1: Rainbow Dash ate flowers; she drank cider as well. (use a semicolon and omit coordinating conjunction)
solution2: Rainbow Dash ate flowers. She drank cider as well. (start a new sentence)
solution3: (insert a comma and a coord conjuction)
*Note that since the subjects of both independent clauses refer to the same noun (Rainbow Dash), you can remove the subject of the 2nd independent clause ("she") in run-on3 to correct it into a simple sentence with two action verbs and two objects.

Now that you know what compound sentences and complex sentences are, you can combine the two to form a 20% cooler compound-complex sentence! And what's more - there is no restriction on order or how many clauses you can put - just remember to use correct commas and conjunctions.

Still reading? Twilight would like to enlighten you on a more convoluted topic: verbs acting as another part of speech.

Verbs acting as nouns? When a verb ending in "ing" functions as a noun, then that's a Gerund.
Every gerund, without exception, ends in "ing". A gerund can only function as a noun, while other verbs with "ing" can function as adjectives/multipart verb as well. A gerund plus modifiers would be a gerund phrase (or gerundial phrase).
example1: Yelling at Sweetie Belle is fun. (The gerund phrase acts like the subject)
example2: Rarity enjoys yelling at Sweetie Belle. (The gerund phrase acts like the direct object)

Verbs acting as adjectives? that's likely a Participle. It can end in "ing"(present participle) OR "ed" (regular past participle) OR in some other fancy way (irregular past participle). Although a present participle can also function as a noun (in which it'll be called a gerund), a participial phrase can only function as adjectives.
example1: Yelling at Sweetie Belle, Rarity finds the act a bit boorish. (The participial phrase describes the subject "Rarity")
example2: Twilight found her friend Rarity yelling at Sweetie Belle. (The participial phrase describes the object "Rarity")
Punctuating participial phrases is similar to, but not the same as, complex sentences.
When the participial phrase comes first, it needs a comma after it. See example1.
When the participial phrase concludes the main clause and is modifying a word right in front, you don't use comma to seperate them. See example2.
However, when a participle phrase concludes a main clause and modifies a word further up in the sentence, you will need a comma.
example3: Rarity trotted to the restaurant, agreeing to bring Sweetie Belle along.

Don't confuse gerund/participial phrases with Infinitive Phrases. Not only can infinitive phrases function as nouns or adjectives, they can function as adverbs as well. An infinitive phrase always begins with "to" + [simple form of the verb], adding objects and/or modifiers as desired.
example1: To yell at Sweetie Belle is Rarity's goal. (The infinitive phrase functions as a noun.)
example2: The best way to survive Rarity's yells is to yell back. (The infinitive phrase functions as an adjective)
example3: Sweetie Belle is yelling at Rarity to challenge the status quo. (The infinitive phrase functions as an adverb)
Rules for punctuation? No comma is needed unless the infinitive phrase interrupts the flow of the independent clause.
example4: All that yelling, to be honest, is getting redundant.

APPENDIX: Other Comma Usage

- Use a comma to set off parenthetical elements (things like introductory elements, apositive phrases, names that are addressed directly, and other explanatory phrases. *Note that unless prepositional phrases are intro or explanatory elements, you don't need to set them off.)
- Use a comma to separate coordinate adjectives.
- Use commas to set off phrases that express contrast

APPENDIX: Who vs Whom

My friend was confused about this, so I made a list of steps to determine which to use.
"slot" stands for a missing word where "who" or "whom" would be inserted.

1. When the slot is in front of a predicate/verb, then the slot is 100% going to be "who". (most common case)
ex. She was the pony who performed the rainboom.
ex. She is Rainbow Dash, who is the best flyer in town.
2. When the slot is in front of a subject, the case is ambiguous. If the follwing predicate is a linking verb, then the slot should be "who" - because "who" is either the subject compliment or the subject of a relative clause.
ex. We would never know who Batmare is.
ex. Rainbow Dash trotted wobbly, who we assume is still drunk. (try taking out "we assume" and you'll see why "who" is correct)
3. Use "whom" otherwise, since it's either going to be the object of the clause or object of a preposition.
ex. Twilight gazed at Rainbow Dash, whom she kissed.
ex. Rainbow Dash, whom Twilight caused the blushing of, returned the kiss.

APPENDIX: Awkward Pronoun that English Invented
If you're confused about its vs it's
It's is a contraction of "it is", "it was", or "it has"
its is usually used as an adjective pronoun (like "my hand", "its hilt"), but sometimes can be a possessive pronoun (like "this blade is mine, and I am its")

While my guide focuses more on grammar, Ezn has made a guide that's more focused on syntax and style. You can find it here.